October 26, 2011

Overall I would say it was a very well received lesson from the students, certainly there was positive feedback in the immediate aftermarth of the lesson. I would say from our point of view also that it was a good experience, and that we each gave a good accoutn of ourselves.

The starter was impressively assembled and challenged each student an appropriate amount. It worked to give a very quick introduction to the topic of plans and elevations as well as a foundation on which to build.

The main of the lesson was also well received, the students were keen and eager to get involved, and although it took extra work to keep some on task and to get a couple motivated to begin with, it was ultimately a success.

Unfortunately due to time constraints (the lesson started 10 minutes late due to late arrivals after assembly) the plenary ended up being slightly rushed which would be the main regret. This was no-ones fault however. What was said was good, in particular the questioning over the relevance of what they had learnt (real world applications for example).

If I were to do the lesson over again, I would spend less time on the main as I feel the vast majority of the students had taken it to its limites, and spend more time on a summary at the end.

Introductory task on board for students on entry to work on whilst settling into the lesson.

Pupils may discuss their thoughts and ideas quietly in small groups (i.e. pairs) whilst doing this.

Greeting students, introducing the task and ensuring there is a swift start to the lesson.

Teacher then presents the remaining two problems and questions the pupils to think about them in the context of the task.

None at this stage as this is an exercise to determine potential initial understanding of all students.

PowerPoint will be coloured to avoid problems to those with dyslexia.

No assessment for right or wrong answers at this stage. Pupils given opportunity to share their thoughts on the problem after 5 minutes, before answer is given.

9:30- 9:35

Discussion of ideas used, spider diagram of conceptions of plans and elevations at this early stage.

Will be contributing to class understanding of plans and elevations. Adding to the debate through raised hands.

Asking pupils for feedback on the previous task and to help construct spider diagram.

None on a level basis. Students problems accessing the material can be addressed on a one to one basis.

Teacher can assess through contribution who has a better initial understanding of the topic.

9:35- 10:00

Pupils given five cubes each and asked to construct a very simple model and then to draw it from the perspective of facing three different sides

Working in pairs to build simple models from construction cubes, starting from 2 cubes and progressing through up to 4 or 5. Drawing the models that they make from the three views.

Initially will demonstrate what is required of the student, and then setting them to work. Assisting students that require further explanation of the task, else discussing findings will students progressing well.

If higher achieving students finish early they will be given an extension sheet of pre-drawn views, and asked to make the shapes.

Assessment will be based on correct drawings of their models. Misconceptions can be addressed as the teacher will have to approve a drawing before an extra cube can be added.

10:00-10:15

Group discussion of findings. Learning assessed through plenary of multi-level questions from teachers (starting from simple: what is this view called? progressing to why would we need to use these?)

Will be invited to answer questions or add to the discussion.

Will stimulate input from students, using a hands up policy unless something specific has been noted throughout the task that the teacher would like a student to raise.

Students who moved on to the extension task may say what extra this told them.

Teacher will be looking for continuing misconceptions from answers and will attempt to address these.

Homework:

Draw a plan of your own bedroom from each of the 3 views we have discussed today.

October 25, 2011

Below is a statistics question I was given in subject studies, followed by how I approached it and my solution.

(9) a) Yesterday I drove 100 miles. My average speed for the first 50 miles was 40mph; my average speed for the last 50 miles was 60mph. What was my average speed for the whole trip?

The temptation here is to immediately find the average of the 2 speeds, however we are spending 2 different amounts of time travelling at these speeds, and so this approach does not work.

Instead we must find how long we have spent travelling the two sections of the trip, then hence the trip as a whole and divide total distance by total time, thusly:

T= 50/40 + 50/60 = 25/12 hours. D= 100 miles

S= D/T .'. S= 100 / (25/12) = 48mph.

b) Here's a related question: Quinten and Xavier have a cycle race. Quinten travels at a constant 15mph. Xavier travels at 10mph uphill, 15mph on level ground and 20mph downhill. The course is evenly divided between uphill, level and downhill sections. Does Quinten win, does Xavier win or do they cross the finishing line at the same time?

We do not need to know exact timings for the course of the race. It is enough to know that the course is evenly divided by distance (not by time).

If we use our s=d/t triangle, Quinten's time taken is d/15.

Xavier's time taken will be 1/3 (d/10 + d/15 + d/20) = 13d/180

d/15 < 13d/180 for all d, therefore Quinten is quicker than Xavier.

This can be seen because Xavier spends longer going slower than Quinten than going quicker, despite the distances being equal, and the speeds being equidistant from Quinten's average.

If we wanted to give a general formula for the overall average speed of a journey broken up into k sections of equal distance, where we travel an average of s1 mph in section 1, s2 mph in section to up to sk mph in section k, we could write this as:

t= Σ[d/(k*sa)] Where the summation is between a=1 and a=k. Hence as s= d/t, ST= d/tT (T= total).

October 04, 2011

Yes I haven't blogged for a fortnight but it has been a busy week both in and out of uni, and so far as priorities go this has not been the highest! (Once again)

The health of my dog has been but the good news is that he is back home now and though on the mend (despite the scars).

I'm going to try to be at least weekly now though so there's that to look forward to.

Observation week this week has been good. It's nice to actually be in a classroom and helping children after all the theory. Not to put a downer on the theory as I'm sure its very important but I am preferring the practical side of the course.

Today I was in a primary school, spending the day in a year 3 classroom. The children were lovely and sweet and the rest but I couldn't cope with the differing demands to secondary schools day in day out so I am sure that I've chosen the right direction with my PGCE!

The student loan company are still being fools of the highest order but at least my bursary is in now, so I have more than £10 left of my overdraft now! Party!

September 19, 2011

Firstly yes I am late setting this blog up, it ideally would have been up before the weekend even, but its been difficult to find a spare minute so it's languished at the bottom of my priorities list.

That out the way, back to school time!

Sort of.

I'm back to having a routine timetable, 9-5ish, hopefully some edges can be cut off of that most days. It's taking some definite adjusting to having to wake up at 7, something I haven't had to commonly do for... 8 years? Thats my primary reason for feeling so tired at the moment.

The other is the sheer amount of information to have to take in at this early stage (and by the sound of it in the midding and late stages too). Its not physically tiring but mentally. Add to that that generally my attention span is not the best and it gets even harder to concentrate towards the end of the day!

Hang on, I'm meant to be a teacher, not a student?

Eh, I'm human!

Joke? I've heard I can't use the e^x one, thats been done. So has log cabin. The cat one doesn't translate as well into text but we can try!

Two cats are sat on a slanted roof. Cat one goes meww! Cat two goes MEWWWWW!

Which cat stays on the roof longest?

...

...

The second cat because it has the largest mew! ( μ )

And my favourite joke (which has nothing to do with maths):

Q: Where do you weigh a whale?

A: At a whaleweigh station!

Moving along as this has taken too much space and there *is* an upload limit.

I've been asked to discuss my opinion on maths busking. Here it is. I think it sounds very interesting, anything that brings maths to a wider public has to be a good thing. If asked would I like to take part in a workshop? then yes! yes I would!

Expect another update in the near future. Hopefully with better paragraph structuring!